Shaving apparatus of the kind indicated above are widely known and e.g. disclosed in WO-A 2004/108368. The apparatus disclosed in said publication has three cutting units, also known as shaving heads, which are provided in a skin contact surface. Each cutting unit comprises one annular shaving portion formed by an external cutting member provided with hair trapping apertures and a rotatably arranged internal cutting member having a number of knives for cutting hair protruding through said hair trapping apertures. The hair trapping apertures are constituted by axially and radially extending slits formed in an annular region of the external cutting member by lamellae radially extending from an inner edge of the annular region to an outer edge of the annular region. Although such a configuration of slits and lamellae has proven to function well as a hair catching structure, it has been found that the configuration causes problems in catching rather long hairs. Such hairs are pushed down against the skin by the lamellae during a shaving movement, as a result of which these rather long hairs cannot enter the slits. Similar shaving apparatus which are provided with two or three annular shaving portions are also known.